An Approximation Pricing Algorithm in an Incomplete Market: A Differential Geometric Approach
The minimal distance equivalent martingale measure (EMM) defined in Goll and Rⁿschendorf (2001) is the arbitrage-free equilibrium pricing measure. This paper provides an algorithm to approximate its density and the fair price of any contingent claim in an incomplete market. We first approximate the infinite dimensional space of all EMMs by a finite dimensional manifold of EMMs. A Riemannian geometric structure is shown on the manifold. An optimization algorithm on the Riemannian manifold becomes the approximation pricing algorithm. The financial interpretation of the geometry is also given in terms of pricing model risk.
Incomplete markets, asset pricing, Riemannian manifold, cross entropy
Finance and Financial Management | Portfolio and Security Analysis
Finance and Stochastics
Gao, Yuan; Lim, Kian Guan; and Ng, Kah Hwa.
An Approximation Pricing Algorithm in an Incomplete Market: A Differential Geometric Approach. (2004). Finance and Stochastics. 8, (4), 501-523. Research Collection Lee Kong Chian School Of Business.
Available at: http://ink.library.smu.edu.sg/lkcsb_research/2545